Slashdot Mirror
Making Change
Roland Piquepaille writes "There are mostly four kinds of coins in circulation in the U.S: 1 cent, 5 cents, 10 cents, and 25 cents. But is it the most efficient way to give back change? This Science News article says that a computer scientist has found an answer. "For the current four-denomination system, [Jeffrey Shallit of the University of Waterloo] found that, on average, a change-maker must return 4.70 coins with every transaction. He discovered two sets of four denominations that minimize the transaction cost. The combination of 1 cent, 5 cents, 18 cents, and 25 cents requires only 3.89 coins in change per transaction, as does the combination of 1 cent, 5 cents, 18 cents, and 29 cents." He also found that change could be done more efficiently in Canada with the introduction of an 83-cent coin and in Europe with the addition of a 1.33- or 1.37-Euro coin. Check this column for more details and references." The paper (postscript) is online.
In France (and probably other countries) most of the prices end in .00 and the taxes are already included (unlike Canada where I live). It's much simpler that way. If only there was a way to convince stores to do that in here...
Opus: the Swiss army knife of audio codec
If only there was a way to convince stores to do that in here...
Its not up to the store, but the law. You must show the PST and GST on every sale in Canada. There was some debate a couple years ago about changing it to hidden costs, but that seems to have been quelled with recent wars and weed laws.
sin(6cos(r)+5A)
Engineers also speak PDE, only in a different dialect.
> In Canada, it's illegal to pay for any good or service, with more than 25 of any given denomination.
What he's talking about can be found in Section 8 of the Currency Act.
Basically it is a no-nuisance law to stop people from doing things like pay fines using pennies. It doesn't say the money can be confiscated...
Many businesses will still except coins if they have been rolled. I know I have paid for movie tickes and extra value meals with rolls of nickles and dimes.
From the statute:
(2) A payment in coins referred to in subsection (1) is a legal tender for no more than the following amounts for the following denominations of coins:
-
Rod (Canadian)
Some egghead thinks "optimal" means "fewest coins returned in change, on average."
/. to come along and rip everything out of context.
No no no. Academia don't have to think about definitions. We just define it that way.
Be seriously, RTFA, people. The important part of this result is not that 18 or 83 cent recommendations. The author did it in jest in reference to the phrase "What this country needs is a good five cent cigar". (cited in the footnote of the paper). Just wait for
The important part of this paper is the second half, the general analysis of methods for finding "optimal" denominations or "optimal" change returns (the first defined to minimize the number of coins returned on average, the second defined as given a set denomination, finding the best way to represent a given amount). It gives asymtotic results. It is more of a computer science excercise then anything else.
W
Engineers also speak PDE, only in a different dialect.
I can't think of an example where that doesn't work in a 1,5,10,25 system
The reason you can't think of any examples in the 1,5,10,25 system is because 10 and 25 are both multiples of five. Therefore whatever you could make with a 25, you could also make with five 5s. So if you would ever have five 5s or two 5s, just use a 25 or a 10, respectively. In 1,40,41 system, 41 is not a multiple of 40 (or vice versa), so it makes finding the optimal number of coins a bit more difficult, since you have to find the optimal number of factors for your change given the different coins. In a 1,5,10,25 system, 5 is already a factor of the other important coins, so you can just count up how many 5s you'd need and then reduce that into 25s and 10s. (Of course the mind usually does it the other way round.)
--
Promoting critical thinking since 1994.
Cecil has the right answer instead of this complete conjecture.
In Australia copper coins (1c & 2c) were taken out of circulation in 1991 (I think). So everything is rounded to a multiple of 5c. The rules for the rounding (set out by law) are:
For cash transactions:
1 & 2 cents -- rounded DOWN to the nearest 10 cents
3 & 4 cents -- rounded UP to the nearest 5 cents
6 & 7 cents -- rounded DOWN to the nearest 5 cents
8 & 9 cents -- rounded UP to the nearest 10 cents
Rounding is on the total value of the bill. Individual items should never be rounded.
And where a consumer pays by cheque, credit card or EFTPOS (electronic transaction) there is no need to round at all.
So basically you win some and you lose some, but it evens out in the end. If you're really diligent, yes you can use it to your advantage, but most people have a life instead.
"Because it's there." - George Mallory, when asked why he wanted to climb Mt Everest, March 18, 1923 (New York Times)
the rounding is only on the final payment at the till, not on individual items. And it's only for cash transactions, not electronic transactions. Sometimes it rounds in your favour, sometimes in the store's favour, but it evens out in the end. Yes, it can be manipulated to save you a cent or two here and there, but anyone doing that should probably worry about getting a life first.
"Because it's there." - George Mallory, when asked why he wanted to climb Mt Everest, March 18, 1923 (New York Times)
Almost. The piece of eight (the Spanish Milled Dollar, worth eight reales) was one of the principal coins of the colonies, but the coin was not broken up. Instead, coins of values equivalent to one-half, one-quarter, and one-eighth of a dollar. One piece of eight was worth on real, eight reales to a dollar...
And now you know.
You can never go home again... but I guess you can shop there.